基于灰导数和预测系数的GM(1,1)优化模型  

Optimizing GM(1,1) Model Based on Grey Derivative and Prediction Coefficient

作　　者：曾柯方 魏勇[1] 

机构地区：[1]西华师范大学数学与信息学院,南充637002

出　　处：《应用泛函分析学报》2014年第1期36-39,共4页Acta Analysis Functionalis Applicata

基　　金：四川省应用基础研究(2008JY0112);四川省高等教育人才培养质量和教学改革(P09264)

摘　　要：针对GM(1,1)模型的适用范围是近指数情况,提出了将优化灰导数与利用原始序列模拟的相对误差平方和最小估计预测系数c相结合的方法,从而得到一种简化计算的新GM(1,1)优化模型,该模型的预测公式x^((0))(k)=ce^(-ak)在形式上比较简洁,并且经严格指数序列从理论上验证了参数a具有白化指数律重合性,预测系数c具有白化系数重合性.For the GM（1,1） model is applicable to nearly exponential case, the method of combining grey derivative optimization with using the simulated minimum sum of relative error square of the original sequence to estimate forecast coefficient c is proposed to construct a new optimization GM（1,1） model of simplified calculation. The prediction formula x（0）（k） = ce^-ak of the model is formally more concise. And the strict index series is theoretically verified that parameter a has white exponential law of coincident property and prediction coefficient c has white coefficient of coincidence property.

关 键 词：GM(1 1)模型 灰导数 预测系数 最小二乘法 白指数律 白化系数重合性 

分 类 号：N941.5[自然科学总论—系统科学]